The nature of the spin liquid ground state of the kagome Heisenberg model and the corresponding materials remains a big unsolved question in the condensed matter physics. Here, I will introduce the progress we have made on this problem by studying an extended kagome model with XXZ anisotropy.  Numerically (by DMRG), we find that the emergence of the spin-liquid phase is independent of the anisotropy of the XXZ interaction. The two spin liquid phases, a chiral and a time-reversal invariant spin liquid in the Heisenberg limit, exist even when an extremely strong easy-axis anisotropy is turned on. Theoretically, we focus on the easy axis limit which admits a faithful lattice gauge description. The dual lattice gauge model is  described by a compact U(1) gauge field coupled with bosonic spinons. Interestingly, we find that in this lattice gauge description,  the underlying physical mechanism of the chiral spin liquid is described by ``gauging" a symmetry protected topological phase. This is a rare example that the spin liquid phase in a realistic model can be analyzed in a controlled way,  which opens a new avenue to study spin liquid physics in physical system.
[1] Yin-Chen He, Subhro Bhattacharjee, Frank Pollmann, and R. Moessner (to be submitted)
[2] Yin-Chen He, Subhro Bhattacharjee, R. Moessner, and Frank Pollmann, arXiv:1506.01645
[3] Yin-Chen He and Yan Chen, PRL 114, 037201 (2015).
[4] Yin-Chen He, D. N. Sheng and Yan Chen, PRL  112, 137202 (2014).